David Cameron has 85% approval among Tory voters according to a new Guardian/ICM opinion poll. Photograph: Parbul/Getty Images

David Cameron on the ropes? Then explain the following. Even after by far the most difficult month in No 10, the prime minister remains the Conservative party's – and the coalition's – strongest electoral asset. This week's Guardian/ICM opinion poll underscored this. Even in the midst of the phone-hacking storm, Cameron's approval ratings among the general public are 10 points ahead of those for Nick Clegg or Ed Miliband. Among his own supporters, Cameron's position remains even more commanding – with 85% approval among Tory voters compared with Clegg's 57% and Miliband's 58% among theirs.

That explains, paradoxically, why the hacking furore is nevertheless so politically important. If Labour were to manage to knock Cameron off his perch over his handling of News International and his involvement with Andy Coulson, they would not merely rock the government on its heels. More important, they would tarnish the coalition's single most voter-friendly asset in what Labour naturally hope is a lasting manner.

Voters tend to stay turned off when they turn sour on a once-admired leader – as happened to Gordon Brown. But that's why Labour has stuck so remorselessly to its Get Cameron theme at every opportunity. Petty and unattractive it may sometimes be, but it makes a lot of crude political sense all the same.

Seen from Westminster as the summer recess starts, though, Labour's efforts have to be judged a failure. Miliband has indisputably had a good crisis, in the course of which he has silenced the mutterings about his leadership and won himself space to enjoy a much better autumn conference season than seemed possible a month ago. But his success should not be exaggerated. Whether he can leverage it into more solid approval still remains to be seen. Meanwhile Cameron has not just survived Miliband's attacks. He has also reasserted his grip on his own party, not least by a marathon performance on Wednesday in the Commons and in a private meeting with his backbenchers. Like it or not, these things matter.

Cameron's resilience in the polls matters too. In spite of a torrid fortnight marked by notable misjudgments and great potential dangers, Cameron is still polling well ahead of his party, while Miliband, for all his efforts, polls well behind his. Don't lose sight of these things. Clearly the summer recess provides an important relief from the Westminster excitements of the past week. It allows Cameron to choose his own agenda more carefully, though Monday's growth figures for what officials optimistically call the royal wedding quarter may be sluggish. Common sense nevertheless suggests that Cameron has survived the worst that Labour can throw at him for the moment.

Yet this may be to underestimate the more subtle unwinding and longer-term costs to the prime minister of the hacking crisis. In the first place, the unanswered questions still have considerable potency. It is all very well asserting the voters want to move on and claiming the doubters are at risk of morphing into conspiracy theorists. Some of that may be true. But an unwelcome answer to the questions still has the power to destroy. Even Watergate took more than two years to unravel. A bit of patience could be in order.

Two issues, in particular, still matter a very great deal. The first is the tightness of the weave between the Cameron Tory party and News International. Those 26 prime ministerial meetings in 15 months since the 2010 election – and many more at ministerial level of which details are likely to emerge next week – speak of a collective cringe towards Rupert Murdoch which cannot be merely dismissed as what Labour did too, especially when the Murdoch camp was so institutionally focused on the BSkyB bid and when the phone-hacking allegations were becoming increasingly serious.

No one in government denies that the term BSkyB passed Cameron's lips sometimes during those meetings, but No 10 is adamant that there was nothing that could be remotely portrayed as negotiation. The weird thing about the Murdochs is that they don't talk business, it is said. Maybe. But the plain fact is also that it looks dishonourable, a touch of the Prince Andrews – not the sort of behaviour that should be expected from ministers offering a new politics.

The second is the relationship with Coulson. The questions surrounding the former Downing Street communications chief can be tortuous, but for Cameron they remain highly threatening. Without a satisfactory explanation of why Coulson was only allowed low-security clearance, for instance, it is inevitable that reasonable people will conclude that No 10 knew he was a problem but were unwilling to face up to it. If there is any truth in the claim – and so far it is only a claim – that Coulson may have been connected to the bugging of a senior Whitehall civil servant, Cameron would find himself in a very tight spot. Cameron concedes the Coulson appointment as his one genuine mistake in the saga, while insisting that it does not raise a wider integrity issue. That may be overly sanguine of him. It would not be the first time.

Neither phone hacking nor Cameron's handling of it is suddenly kicked into the long grass. Into the light rough, maybe. All the issues, though, are going to return with regularity over the coming months, culminating in the Leveson report.

The sheer proliferation of other inquiries announced this week is evidence of contradictory impulses: these range from a high-minded, slightly old-fashioned desire to discover the truth and draw the right conclusions, to something close to ministerial panic. Policing, in particular, is now entangled in a series of inquiries which are potentially very significant, but which lack much logical coherence of any kind other than the desire to shut the subjects down. If nothing else, the lesson of the last three weeks that Cameron needs to learn is to sharpen up his team.

Politically, the question about the phone-hacking crisis is this: where will it ultimately stand on the spectrum of damage that stretches from Watergate, which brought a president down, to the Bernie Ecclestone deal, a sordid error which caused Tony Blair not much more than embarrassment? Right now, the answer is that no one knows. Phone hacking retains the potential to be either. Cameron has handled much of the crisis with his usual reliable feel for modern politics. But he has also revealed a what-the-hell insouciance that may yet prove his achilles' heel.

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